In his 2004 paper How Can we Construct a Science of Consciousness? Dave Chalmers says,

Where there is systematic covariation between two classes of data, we can expect systematic principles to underlie and explain the covariation. In the case of consciousness, we can expect systematic bridging principles to underlie and explain the covariation between third-person data and first-person data. A theory of consciousness will ultimately be a theory of these principles…

In the third-person facts are all of the functional characterizations typically appealed to by the Lewisian. In the first-person data we find such things as that blue is more like purple than it is like orange and that pain has a certain phenomenal feel, etc. What kind of fundamental principles can we expect? Chalmers gives us a couple of examples in his Facing Up to the Problem of Consciousness. First he postulates “the principle of structural coherence” which he characterizes as;

This is a principle of coherence between the structure of consciousness and the structure of awareness. Recall that “awareness” was used earlier to refer to the various functional phenomena that are associated with consciousness. I am now using it to refer to a somewhat more specific process in the cognitive underpinnings of experience. In particular, the contents of awareness are to be understood as those information contents that are accessible to central systems, and brought to bear in a widespread way in the control of behavior.

In short, then, phenomenal consciousness correlates with what states we access or are aware of ourselves as being in. The second principle is that of “functional invariance” which he characterizes as follows;

This principle states that any two systems with the same fine-grained functional organization will have qualitatively identical experiences. If the causal patterns of neural organization were duplicated in silicon, for example, with a silicon chip for every neuron and the same patterns of interaction, then the same experiences would arise.

These principles are not fundamental but can be explained by some more basic principle and here Chamers offers the dual aspect of information principle;

This leads to a natural hypothesis: that information (or at least some information) has two basic aspects, a physical aspect and a phenomenal aspect. This has the status of a basic principle that might underlie and explain the emergence of experience from the physical. Experience arises by virtue of its status as one aspect of information, when the other aspect is found embodied in physical processing.

At this point one may wonder why we shouldn’t identify the phenomenal properties with the physical properties…Chalmers, in the 2004 paper, says this;

…What would this entail about the relationship between physical processes and consciousness? The existence of such principles is compatible with different philosophical views. One might regard the principles as laws connecting two fundamentally different domains (Descartes 1641/1996; Popper and Eccles 1977). One might regard them as laws connecting two aspects of the same thing (Lockwood 1989; Chalmers 1996). Or one might regard them as grounding an identification between properties of consciousness and physical properties (Smart 1959; Papineau 2002). Such principles could also be combined with different views of the causal relation between physical processes and consciousness (see Chalmers 2002).

So Dave does acknowledge that one might take these correlations to ground an identity claim. Interestingly he seems to take the way that the identity claim will be established as via thinking about parsimony. I suppose that Ned will argue that asserting the identity allows for explanations that we would not have otherwise. Both of these seem like fine reasons to posit the identity. What will the 2-D theorist say? it seems to me that the principle of structural coherence is exactly what gives us the functional foothold that we need to identify the biological basis of experience. What we need then is to determine whether the principle of structural coherence gives us any reason to think that some kind of higher-order theory is right.

UPDATE: It just occurred to me one might use the above kind of considerations to argue that Maria will be able to make the deductions from P to Q (and vice versa) a priori…if so then that would be an independent argument for the identity of the two sets of properties.